What is the smallest possible constant of a 3×3 magic square containing nine distinct non-composite numbers only?

(In reply to

solution(?) by Justin)

Right - I just modified my program to find all the minimum constants (zeros) for a,b,c <21. There are two solutions (discounting rotations and reflections)

Here they are below.

I also verified Justin's complete solutions: min constant = 111 for non-neg terms a,b,c (-50, 50) and the constant = 177 as the minimum for strictly primes for a, b, c all between -1000,1000. (I found only 1 solution + rotations etc. in each case, once again, those he gave.)

That being said, I have no idea how to prove this is a minimum for all a,b,c.

0

2 -7 5

3 0 -3

-5 7 -2

0

2 -5 3

1 0 -1

-3 5 -2

*Edited on ***September 29, 2018, 8:22 pm**